1. Mathematical Description of Continuous-Time Signals
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2. Typical Continuous-Time Signals
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3. Continuous vs Continuous-Time Signals
All continuous signals that are functions of time are
continuous-time but not all continuous-time signals are
continuous
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4. Continuous-Time Sinusoids
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5. Continuous-Time Exponentials
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6. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
Complex Sinusoids
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7. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Signum Function
Precise Graph
Commonly-Used Graph
The signum function, in a sense, returns an indication of
the sign of its argument.
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8. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Unit Step Function
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9. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Unit Step Function
The unit step function can mathematically describe a
signal that is zero up to some point in time and non-
zero after that.
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10. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Unit Ramp Function
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11. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Unit Ramp Function
Product of a sine wave and a ramp function.
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12. Introduction to the Impulse
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13. Introduction to the Impulse
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14. The Unit Step and Unit Impulse
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15. Graphical Representation of the Impulse
The impulse is not a function in the ordinary sense because its
value at the time of its occurrence is not defined. It is represented
graphically by a vertical arrow. Its strength is either written beside
it or is represented by its length.
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16. Properties of the Impulse
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17. The Unit Periodic Impulse
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18. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
The Periodic Impulse
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19. The Unit Rectangle Function
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20. Combinations of Functions
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21. Shifting and Scaling Functions
Let a function be defined graphically by
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22. Shifting and Scaling Functions
Amplitude Scaling,
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23. Shifting and Scaling Functions
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24. Shifting and Scaling Functions
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25. Shifting and Scaling Functions
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26. Shifting and Scaling Functions
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27. Shifting and Scaling Functions
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28. Shifting and Scaling Functions
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29. Shifting and Scaling Functions
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30. Shifting and Scaling Functions
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31. Shifting and Scaling Functions
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32. Shifting and Scaling Functions
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33. Shifting and Scaling Functions
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34. Shifting and Scaling Functions
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35. Shifting and Scaling Functions
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36. Shifting and Scaling Functions
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37. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
Differentiation
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38. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
Integration
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39. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
Even and Odd Signals
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40. Even and Odd Parts of Functions
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41. Even and Odd Parts of Functions
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42. Products of Even and Odd Functions
Two Even Functions
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43. Products of Even and Odd Functions
An Even Function and an Odd Function
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44. Products of Even and Odd Functions
An Even Function and an Odd Function
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45. Products of Even and Odd Functions
Two Odd Functions
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46. Integrals of Even and Odd Functions
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47. Integrals of Even and Odd Functions
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48. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
Periodic Signals
A function that is not periodic is aperiodic.
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49. Sums of Periodic Functions
The period of the sum of periodic functions is the least common
multiple of the periods of the individual functions summed. If the
least common multiple is infinite, the sum function is aperiodic.
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50. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
ADC Waveforms
Examples of waveforms which
may appear in analog-to-digital converters. They can be described by a periodic repetition of a ramp returned to zero by a negative step or by a periodic repetition of a triangle-shaped function.
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51. Signal Energy and Power
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52. Signal Energy and Power
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl

53. Signal Energy and Power
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54. Signal Energy and Power
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55. Signal Energy and Power
A signal with finite signal energy is
called an energy signal.
A signal with infinite signal energy and
finite average signal power is called a
power signal.
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56. Signal Energy and Power
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